Data Sufficiency

What is the value of x² - y²?

1) x + y = 2x
2) x - y = 0

Target question: What is the value of x² - y²?
IMPORTANT: Notice that x² - y² is a DIFFERENCE OF SQUARES, which we can factor to get: (x + y)(x - y).

Statement 1: x + y = 2x
Notice what happens if we rearrange the terms here.
Subtract x from both sides to get: y = x
Subtract y from both sides to get: 0 = x - y
This means that x² - y² = (x + y)(x - y) = (x + y)(0) = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x - y = 0
This means that x² - y² = (x + y)(x - y) = (x + y)(0) = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

What is the value of x² - y²?

1) x + y = 2x
2) x - y = 0

ANOTHER approach:

Target question: What is the value of x² - y²?

Statement 1: x + y = 2x
Notice what happens if subtract x from both sides.
We get: y = x
If x = y, then x² = y², which means x² - y² = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x - y = 0
If x - y = 0, then x = y
If x = y, then x² = y², which means x² - y² = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent